398 BELL SYSTEM TECHNICAL JOURNAL 



where 



m = C1C2C3C4 J 



The low-frequency current deUvered to the receiver through the low- 

 frequency output circuit proper differs from a as given by (9) by a 

 constant factor only. 



From the foregoing we note that 



\s - fxa = -T-— — (11) 



and that the "instantaneous frequency" of the intermediate high- 

 frequency wave (4) is 



'•^o + r^- (12) 



Hereinafter, without any loss of generality, we suppose that 

 — 1 = s{t) ^ 1. Consequently the intermediate frequency-modulated 

 wave has a frequency variation lying between ± X/(l -|- m), whereas 

 in the incoming frequency-modulated wave, the frequency variation 

 lies between ± X. 



We note also from (9) that if the parameter ni is large compared 

 with unity, the low-frequency received wave is approximately given by 



o- = -5. (13) 



n 



The recovered signal is thus (for large values of m) seen to be inde- 

 pendent of the amplitude, E, of the incoming high-frequency wave; 

 therefore, the system is insensitive to "fading." 



II 



We now take up the problem of calculating the relative low-frequency 

 noise and signal powers, the ratio of which is of fundamental importance 

 in appraising the merits of the receiving circuit. In this we shall 

 closely follow the methods developed in Section IV (Ref.). 



We suppose that at terminals 1, 1 there enters, in addition to the 

 signal, a typical noise element 



a„ exp (i(coc + oin)t + idn). (14) 



